Descartes' life
Descartes' father was a member of the local council of Brittany and a judge of the local court. Descartes lived a carefree life in his childhood. He was sickly when he was a child, and has been taken care of by a nanny since his mother died. He is full of curiosity about the things around him. Seeing that he has the temperament of a philosopher, his father affectionately called him a "little philosopher".
My father hoped Descartes would become a theologian in the future, so when he was eight years old, he sent him to the Jesuit school in Lafleur for a classical education. In order to take care of his weak body, the school chartered him not to be bound by school rules, not to go to school in the morning and to study in bed. So he has developed the habit of being quiet and good at thinking since he was a child.
Descartes 16 12 went to the University of Poitiers to study law, and received his doctorate four years later. After Descartes finished his studies in 16 16, he deviated from his family's professional tradition and began to explore the road of life. He joined the army and wanted to take the opportunity to travel around Europe and broaden his horizons.
Several experiences during this period had a great influence on him. Once, Descartes was walking in the street and came across a notice offering a reward for a math problem. Two days later, Descartes actually solved this problem, which attracted the attention of the famous scholar Pickman. Pickermann introduced Descartes to the latest development of mathematics and gave him many problems to be studied.
With the communication with Pickman, Descartes had a full understanding of his mathematical and scientific abilities, and he began to seriously explore whether there were universal methods similar to mathematics in order to acquire real knowledge.
It is said that Descartes had three strange dreams in one night. The first dream was that Descartes was blown by the storm where the wind could not; The second dream is that he got the key to open the treasure house of nature; The third dream is that he opened up the road to real knowledge. These three strange dreams strengthened his confidence in establishing a new theory. This day is a turning point of Descartes' thought, and some scholars have designated this day as the birth date of analytic geometry.
However, the long-term military life made Descartes feel tired. He returned to China in 162 1, when civil strife was taking place in France, so he traveled to Holland, Switzerland, Italy and other places. /kloc-returned to Paris in 0/625 and moved to the Netherlands in 0/628.
During more than 20 years in the Netherlands, Descartes has conducted in-depth research in the fields of philosophy, mathematics, astronomy, physics, chemistry and physiology, and maintained close contact with major European scholars through mathematician Father Mei Sen. Almost all his major works were completed in the Netherlands.
1628, Descartes wrote The Principles of Guiding Philosophy, 1634, and he completed On the World based on Copernicus. This book summarizes his views on philosophy, mathematics and many natural science problems. 1637, Descartes wrote three papers on refractive optics, meteorology and geometry in French, and wrote the preface "Methodology of Correctly Applying Reason and Pursuing Truth in Science", which is called methodology for short in the history of philosophy and published anonymously in Leiden on June 8. 164 1 published Metaphysical Meditation, and 1644 published Philosophical Principles and other important works.
/kloc-in the winter of 0/949, Descartes came to Stockholm at the invitation of Queen Christina and served as a court philosopher to teach Queen Christina. Because he is weak, he can't adapt to the climate there. 1650 suffered from pneumonia at the beginning and died in February of the same year.
The birth of analytic geometry
In Descartes' time, algebra is still a relatively new science, and geometric thinking still occupies a dominant position in the minds of mathematicians. 1637, Descartes published Geometry, which confirmed Descartes' position in the history of mathematics.
The Renaissance enabled European scholars to inherit the geometry of ancient Greece and accept the algebra introduced from the East. With the development of science and technology, describing sports with mathematical methods has become the central issue of concern. Descartes analyzed the advantages and disadvantages of geometry and algebra, and said that he would "seek another method that contains the advantages of these two sciences without their disadvantages".
In the first volume of Geometry, he used the distance from a point on a plane to two fixed straight lines to determine the distance of the point, and used coordinates to describe the point in space. He further founded analytic geometry, showing that geometric problems can not only be reduced to algebraic form, but also be discovered and proved through algebraic transformation.
Descartes transformed geometric problems into algebraic problems and put forward a unified drawing method of geometric problems. To this end, he introduced the concepts of unit line segment, addition, subtraction, multiplication and division of line segments and square root, thus linking line segments with quantity. Through the relationship between line segments, he "found two ways to represent the same quantity, which will form an equation", and then drew according to the relationship between line segments represented by the solution of the equation.
In the second volume, when Descartes used this new method to solve the Pappus problem, he took a straight line as the baseline on the plane, set a starting point for it, and selected another straight line intersecting with it, which was equivalent to the X axis, the origin and the Y axis, respectively, to form an oblique coordinate system. Then the position of any point on the plane can be uniquely determined by (x, y). The Pappus problem becomes a quadratic indefinite equation with two unknowns. Descartes pointed out that the number of equations has nothing to do with the choice of coordinate system, so curves can be classified according to the number of equations.
The book Geometry puts forward the main ideas and methods of analytic geometry, which marks the birth of analytic geometry. Since then, mankind has entered the stage of variable mathematics.
In the third volume, Descartes pointed out that the roots of an equation can be as many as its times, and also put forward the famous Descartes sign rule: the maximum number of positive roots of an equation is equal to the number of times its coefficient changes sign; The maximum number of its negative roots (which he called false roots) is equal to the number of times the symbol remains unchanged. Descartes also improved the symbol system created by Vader, using a, b, c, … to represent known quantities and x, y, z, … to represent unknown quantities.
The appearance of analytic geometry has changed the trend of separation between algebra and geometry since ancient Greece, unified the "number" and "shape" which are opposite to each other, and combined geometric curves with algebraic equations. Descartes' creation laid the foundation for the creation of calculus, thus opening up a broad field of variable mathematics.
As Engels said: "The turning point in mathematics is Cartesian variables. With variables, motion enters mathematics, with variables, dialectics enters mathematics, with variables, differentiation and integration become necessary immediately. "
Descartes' achievements in other scientific fields
Descartes made a useful contribution to physics by virtue of genius intuition and strict mathematical reasoning. Descartes began to read Kepler's optical works from 16 19, and always paid attention to the lens theory. He also participated in the study of the essence, reflection and refractive index of light and lens grinding from both theoretical and practical aspects. He believes that the theory of light is the most important part of the whole knowledge system.
Descartes used his coordinate geometry to engage in optical research, and put forward the theoretical derivation of refraction law for the first time in Refractive Optics. He thinks that light is the propagation of pressure in the ether. From the viewpoint of light emission theory, he calculated the reflection, refraction and total reflection of light on the interface between two media by using the model of tennis ball hitting cloth, and thus deduced the law of refraction for the first time under the assumption that the velocity component parallel to the interface is unchanged. But his hypothesis is wrong, and his deduction leads to the wrong conclusion that the speed of light increases when it enters the dense medium from the sparse medium. He also made an optical analysis of people's eyes, explained that the cause of vision impairment was the deformation of the lens, and designed a lens to correct vision.
In mechanics, Descartes developed Galileo's theory of motion relativity. For example, in the book "Principles of Philosophy", a vivid example of the watch wheel of a sailor's pocket watch on a sailboat is given to illustrate the reason that reference objects need to be selected in motion and stillness.
In the second chapter of Principles of Philosophy, Descartes first expressed the law of inertia in the form of the first law and the second law of nature: as long as an object starts to move, it will continue to move at the same speed and in the same straight line direction until it meets some obstacles or deviations caused by external reasons. Here, he emphasized the linearity of inertial motion that Galileo did not explicitly express.
In this chapter, he also clearly put forward the law of conservation of momentum for the first time: the total amount of matter and motion will never change. Descartes made a preliminary study on collision and centrifugal force, which created conditions for Huygens' success later.
Descartes applied his mechanistic viewpoint to celestial bodies, developed the theory of cosmic evolution and formed his theory of the origin and structure of the universe. He believes that it is easier to understand things from the perspective of development than just from the existing form. He founded the vortex theory. He thinks that there is a huge vortex around the sun, which drives the planets to keep running. The particles of matter are in a unified vortex, which distinguishes the three elements in motion: earth, air and fire. Earth forms planets, and fire forms the sun and stars.
He believes that the motion of celestial bodies comes from inertia and the pressure of some cosmic material vortex on celestial bodies, and there must be a celestial body in the center of various vortex sizes, so this hypothesis is used to explain the interaction between celestial bodies. Descartes' etheric vortex model of the origin of the sun relies on mechanics instead of theology for the first time to explain the formation process of celestial bodies, the sun, planets and satellite comets. , a century earlier than Kant's nebula theory, is the most authoritative cosmology in17th century.
Descartes' theory of celestial evolution, vortex model and close interaction, like his whole ideological system, on the one hand, is characterized by rich physical thoughts and rigorous scientific methods, which played a role in opposing scholasticism, inspiring scientific thinking and promoting the progress of natural science at that time, and had a far-reaching impact on the thoughts of many natural scientists; On the other hand, it often stays in the intuitive and qualitative stage, rather than starting from quantitative experimental facts, so some concrete conclusions often have many defects, which have become the main opposites of Newtonian physics and caused extensive debates.
Descartes also made many commendable innovations in other scientific fields. He also put forward the theory of stimulus response, which made a certain contribution to physiology.
The originator of modern science
Descartes was one of the founders of modern European philosophy, and Hegel called him "the father of modern philosophy". He formed his own system and combined materialism and idealism, which had a far-reaching influence in the history of philosophy.
Descartes is a dualist in philosophy and regards God as the creator. But Descartes was a mechanical degenerate in natural science, which was of progressive significance at that time.
Descartes believes that matter is composed of particles, and particles are the only entities; The essence of matter is its spatial extensiveness, and mechanical movement, that is, position change, is the only movement form of matter; All natural phenomena, all material properties (including color. Fragrance, hardness, heat, etc. ) are produced by the mechanical interaction of material particles; With the movement of matter (space) and (machinery), the whole world can be built according to the natural laws of material movement itself, without the care of God.
This mechanistic view of nature has dominated natural science for more than two centuries. Descartes not only acknowledged the objective existence of the material world, but also acknowledged the absolute view of material movement. He declared: "Give me material things and exercise, and I can create this world." . So Descartes is one of the outstanding representatives of dialectics.
Descartes emphasized that the purpose of science is to benefit mankind and make man the master and ruler of nature. He opposed scholasticism and theology as "hypocritical science", and advocated re-examining knowledge, putting forward systematic questioning methods and doubting everything. But he also put forward the philosophical proposition of "I think, therefore I am".
He said: I can doubt everything except "I doubt", which shows that there is a skeptical me (that is, my mind) that exists independently. He further pointed out the difference between mind and matter: the mind can think without occupying space; Matter occupies space without thinking; The two do not decide each other and do not derive from each other. This is the essence of Descartes' dualism philosophy. He also tried to prove the existence of God. He believes that both matter and spirit are dominated by God, and God is perfect. He completely separated matter from spirit, and divided philosophy into "doing school" and "physics".
Descartes is a mechanist. He believes that the universe is full of matter and motion, whether in the sky or on the earth. He defined motion as displacement motion (that is, mechanical motion). He put forward the principle of conservation of motion to keep the universe in eternal mechanical motion. There is no essential difference between man-made machines and natural objects. The difference is that every part of the artificial machine is clearly seen by us. He believes that the human body is essentially a machine and all its functions can be explained by mechanics.
Descartes' methodology has an important influence on the later development of physics. On the basis of ancient deductive method, he created mathematical deductive method: based on rationalism, starting from self-evident intuitive axioms, using mathematical logic to draw conclusions. This method, combined with experimental induction advocated by Bacon, has become an important method in physics, especially theoretical physics, through the comprehensive application of Huygens and Newton. Descartes solved geometric problems with algebra and established the foundation of coordinate geometry, namely analytic geometry, which is one of the most successful examples of his universal method.
There are two other points worth noting in Descartes' methodology. First, he is good at explaining physical phenomena with intuitive "models". For example, the tennis model is used to explain the refraction of light; Use "crutches for the blind" to vividly describe the instantaneous transmission of light information along matter; The rainbow phenomenon is simulated and successfully explained with a glass ball filled with water. Secondly, he advocates the use of hypotheses and hypothetical methods, such as vortex theory in the theory of cosmic structure. In addition, he also put forward the principle of "universal suspicion". This principle played a great role in opposing church rule, advocating authority, advocating rationality and advocating science under the historical conditions at that time.
Descartes can be said to be one of the most influential masters of European philosophy and science in the17th century and beyond, and is known as "the ancestor of modern science".